Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

On a piece of paper, graph [tex]$y\ \textless \ \frac{3}{4} x+2$[/tex]. Then determine which answer choice matches the graph you drew.

A. Graph A
B. Graph B
C. Graph C
D. Graph D


Sagot :

To tackle the problem, let's first analyze the inequality given and translate it into a graph.

1. Understand the inequality:
[tex]\[ y < \frac{3}{4}x + 2 \][/tex]
This inequality represents a region below the line \( y = \frac{3}{4}x + 2 \).

2. Graph the boundary line \( y = \frac{3}{4}x + 2 \):
- The slope-intercept form of the equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Here, the slope \( m \) is \( \frac{3}{4} \) and the y-intercept \( b \) is \( 2 \).

- To graph this line, start at the y-intercept (0, 2) on the y-axis.
- From (0, 2), use the slope \(\frac{3}{4}\):
- Move up 3 units (rise) and to the right 4 units (run), arriving at the point (4, 5).

- Plot these points and draw a straight line through them. This line will be dashed, as the inequality is strict (\(<\) instead of \(\leq\)), indicating that points on the line are not included in the solution set.

3. Shade the correct region:
- Since the inequality is \( y < \frac{3}{4}x + 2 \), the region to be shaded is below the line.

4. Identify the correct graph from the choices:
- Look for the graph that features:
- A dashed line representing \( y = \frac{3}{4}x + 2 \).
- Shading below this line.

Now, examining the answer choices provided, you should look for the one that matches these criteria. Given that I don't have the actual graphs in front of me, you need to compare the described criteria to the graph choices (A, B, C, D).

Upon comparing, the correct graph will:
- Have a dashed boundary line.
- Reflect the slope 3/4, intercepting the y-axis at 2.
- Shade the region below this line.

Select the answer choice (Graph A, B, C, or D) that matches this description.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.